Finite Group Databasebeta

← #10606015

Subgroups — #10606015

Order 640.

400 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#383C211yesmaximal, characteristic, complemented
2#65229C211yesmaximal, characteristic
3#65218C211yesmaximal, characteristic, complemented
4#64963C211yesmaximal, characteristic
5#64962C211yesmaximal, characteristic
6#64958C211yesmaximal, characteristic
7#64957C211yesmaximal, characteristic
8#64957C211yesmaximal, characteristic
9#64953C211yesmaximal, characteristic
10#64950C211yesmaximal, characteristic, complemented
11#64949C211yesmaximal, characteristic, complemented
12#64947C211yesmaximal, characteristic, complemented
13#64946C211yesmaximal, characteristic, complemented
14#64940C211yesmaximal, characteristic, complemented
15#64935C211yesmaximal, characteristic, complemented
16C22×C4×D5C2211yescharacteristic
17C22×Dic10C2211yescharacteristic
18C2×C42×C5C2211yescharacteristic
19C2×#685C2211yescharacteristic
20C2×#685C2211yescharacteristic
21C2×#685C2211yescharacteristic
22C2×#685C2211yescharacteristic
23C2×#685C2211yescharacteristic
24C2×#685C2211yescharacteristic
25C2×C4⋊Dic5C2211yescharacteristic
26C2×C4⋊Dic5C2211yescharacteristic
27C2×C4⋊Dic5C2211yescharacteristic
28C2×#683C2211yescharacteristic
29C2×#683C2211yescharacteristic
30C2×#683C2211yescharacteristic
31C2×#683C2211yescharacteristic
32C2×C4×Dic5C2211yescharacteristic
33C5×#95C2211yescharacteristic
34C5×#95C2211yescharacteristic
35C5×#95C2211yescharacteristic
36C5×#95C2211yescharacteristic
37C5×#95C2211yescharacteristic
38C5×#95C2211yescharacteristic
39#3963C2211yescharacteristic
40#3963C2211yescharacteristic
41#3963C2211yescharacteristic
42#3963C2211yescharacteristic
43#3963C2211yescharacteristic
44#3963C2211yescharacteristic
45#3963C2211yescharacteristic
46#3963C2211yescharacteristic
47#3963C2211yescharacteristic
48#3963C2211yescharacteristic
49#3963C2211yescharacteristic
50#3963C2211yescharacteristic
51#2764—51nomaximal, Sylow
52C23×D5C2311yescharacteristic
53C22×C4×C5C2311yescharacteristic
54C22×C4×C5C2311yescharacteristic
55C22×C4×C5C2311yescharacteristic
56C22×C4×C5C2311yescharacteristic
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×Dic5C2311yescharacteristic
61C22×Dic5C2311yescharacteristic
62C22×Dic5C2311yescharacteristic
63C22×Dic5C2311yescharacteristic
64C22×Dic5C2311yescharacteristic
65C22×Dic5C2311yescharacteristic
66C22×Dic5C2311yescharacteristic
67C2×C4×D5—22no—
68C2×C4×D5—41no—
69C2×C4×D5—41no—
70C2×Dic10—22no—
71C2×Dic10—22no—
72C2×Dic10—41no—
73C42×C5—22no—
74#685—22no—
75#685—22no—
76#685—22no—
77#685—22no—
78#685—41no—
79#685—41no—
80C4⋊Dic5—41no—
81C4⋊Dic5—41no—
82C4⋊Dic5—41no—
83#683—41no—
84#683—41no—
85#683—41no—
86#683—41no—
87C4×Dic5—22no—
88#400—51no—
89#400—51no—
90#398—51no—
91#398—51no—
92#397—51no—
93#393—51no—
94#391—51no—
95#391—51no—
96#388—51no—
97#388—51no—
98#385—51no—
99#385—51no—
100#383—51no—
101#383D511yescharacteristic, complemented
102#381—51no—
103C23×C5C2411yescharacteristic
104C22×D5—21no—
105C22×D5—21no—
106C22×D5—21no—
107C22×D5—21no—
108C22×D5—21no—
109C22×D5—21no—
110C22×D5#4112yes—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5#4112yes—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—21no—
140C2×Dic5—21no—
141C2×Dic5—21no—
142C2×Dic5—21no—
143C2×Dic5—21no—
144C2×Dic5—21no—
145C2×Dic5—21no—
146C2×Dic5—21no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5#4112yes—
153C4×D5—44no—
154Dic10—44no—
155C22×Q8—51no—
156C23×C4—51no—
157C2×C4⋊C4—51no—
158C2×C4⋊C4—51no—
159C2×C4⋊C4—51no—
160C2×C4⋊C4—51no—
161C2×C4⋊C4—51no—
162C2×C4⋊C4—51no—
163C2×C4⋊C4—51no—
164C2×C22⋊C4—51no—
165C2×C22⋊C4—51no—
166C2×C22⋊C4—51no—
167C2×C22⋊C4—51no—
168C2×C22⋊C4—51no—
169C2×C22⋊C4—51no—
170C2×C42—51no—
171C2×C42C2×D511yescharacteristic
172#95—51no—
173#95—51no—
174#95—51no—
175#95—51no—
176#95—51no—
177#95—51no—
178#95—51no—
179#95—51no—
180#95—51no—
181#95—51no—
182#95—51no—
183#95—51no—
184#95C2×D511yescharacteristic
185#95C2×D511yescharacteristic
186#95C2×D511yescharacteristic
187#95C2×D511yescharacteristic
188#95C2×D511yescharacteristic
189#95C2×D511yescharacteristic
190C22×C5C2×#4111yescharacteristic
191C22×C5C2×#4111yescharacteristic
192C22×C5C2×#4111yescharacteristic
193C22×C5H(5,𝔽2)11yescharacteristic
194C22×C5H(5,𝔽2)11yescharacteristic
195C22×C52−1+411yescharacteristic
196C22×C52−1+411yescharacteristic
197C2×D5—22no—
198C2×D5—22no—
199C2×D5—22no—
200C2×D5—41no—
201C2×D5—41no—
202C2×D5—41no—
203C2×D5—41no—
204C4×C5—22no—
205C4×C5—41no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5—41no—
209C4×C5—41no—
210C4×C5—41no—
211Dic5—22no—
212Dic5—41no—
213Dic5—41no—
214Dic5—41no—
215Dic5—41no—
216Dic5—41no—
217Dic5—41no—
218C24—51no—
219C2×Q8—102no—
220C2×Q8—102no—
221C2×Q8—201no—
222C22×C4—51no—
223C22×C4—51no—
224C22×C4—51no—
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—51no—
229C22×C4—102no—
230C22×C4—201no—
231C22×C4—201no—
232C22×C4C22×D511yescharacteristic
233C22×C4C22×D511yescharacteristic
234C22×C4C22×D511yescharacteristic
235C22×C4C22×D511yescharacteristic
236C22×C4C22×D511yescharacteristic
237C22×C4C22×D511yescharacteristic
238C22×C4C22×D511yescharacteristic
239C4⋊C4—201no—
240C4⋊C4—201no—
241C4⋊C4—201no—
242C4⋊C4—201no—
243C4⋊C4—201no—
244C4⋊C4—201no—
245C4⋊C4—201no—
246C22⋊C4—102no—
247C22⋊C4—102no—
248C22⋊C4—102no—
249C22⋊C4—102no—
250C22⋊C4—201no—
251C22⋊C4—201no—
252C42—22no—
253C42—102no—
254C2×C5#53811yescharacteristic
255C2×C5#54211yescharacteristic
256C2×C5#54211yescharacteristic
257C2×C5#55111yescharacteristic
258C2×C5#55211yescharacteristic
259C2×C5#55211yescharacteristic
260C2×C5#56311yescharacteristic
261D5—42no—
262C23—52no—
263C23—101no—
264C23—101no—
265C23—101no—
266C23—101no—
267C23—101no—
268C23—101no—
269C23C23×D511yescharacteristic
270Q8—204no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—52no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—101no—
305C2×C4—101no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—101no—
310C2×C4—101no—
311C2×C4—101no—
312C2×C4—204no—
313C2×C4#70912yes—
314C5#276411yescharacteristic, complemented, Sylow
315C22—102no—
316C22—102no—
317C22—102no—
318C22—201no—
319C22—201no—
320C22—201no—
321C22—201no—
322C22C2×#70911yescharacteristic
323C22D5×#4111yescharacteristic
324C22D5×#4111yescharacteristic
325C22#414911yescharacteristic
326C22#414911yescharacteristic
327C22#415011yescharacteristic
328C22#415011yescharacteristic
329C4—22no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—102no—
337C4—201no—
338C4—201no—
339C4—201no—
340C4—201no—
341C4—201no—
342C4—201no—
343C2—202no—
344C2#6586111yescharacteristic
345C2#6586311yescharacteristic
346C2#6586811yescharacteristic
347C2#6603811yescharacteristic
348C2#6604211yescharacteristic
349C2#6604411yescharacteristic
350C2#6604611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#383C2
prime radicalC23×D5C23
hypercenter#383D5
hypocenterC5#2764
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #383

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×#383C2semidirect
3. #65218C2semidirect
10. #64950C2semidirect
11. #64949C2semidirect
12. #64947C2semidirect
13. #64946C2semidirect
14. #64940C2semidirect
15. #64935C2semidirect
101. #383D5semidirect
314. C5#2764semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#3832
#652292
#652182
#649632
#649622
#649582
#649572
#649532
#649502
#649492
#649472
#649462
#649402
#649352
#27645